Year: 2025
Type: article
Abstract: We propose a new approach to conjugation-invariant random permutations. Namely, we explain how to construct uniform permutations in given conjugacy classes from certain point processes in the plane. This enables the use of geometric tools to study various statistics of such permutations. For their longest decreasing subsequences, we prove universality of the $$2\sqrt{n}$$ 2 n asymptotic. For Robinson–Schensted shapes, we prove universality of the Vershik–Kerov–Logan–Shepp limit shape, thus solving a conjecture of Kammoun. For the number of records, we establish a phase transition phenomenon as the number of fixed points grows. For pattern counts, we obtain an asymptotic normality result, partially answering a conjecture of Hamaker and Rhoades.
Author: Victor Dubach
Institution: Uppsala University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Uppsala Universitet
OpenAlex ID: W4416042856